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1 June 2011 Inductive construction of the p-adic zeta functions for noncommutative p-extensions of exponent p of totally real fields
Takashi Hara
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Duke Math. J. 158(2): 247-305 (1 June 2011). DOI: 10.1215/00127094-1334013

Abstract

We construct the p-adic zeta function for a one-dimensional (as a p-adic Lie extension) noncommutative p-extension F of a totally real number field F such that the finite part of its Galois group G is a p-group of exponent p. We first calculate the Whitehead groups of the Iwasawa algebra Λ(G) and its canonical Ore localization Λ(G)S by using Oliver and Taylor's theory of integral logarithms. This calculation reduces the existence of the noncommutative p-adic zeta function to certain congruences between abelian p-adic zeta pseudomeasures. Then we finally verify these congruences by using Deligne and Ribet's theory and a certain inductive technique. As an application we prove a special case of (the p-part of) the noncommutative equivariant Tamagawa number conjecture for critical Tate motives.

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Takashi Hara. "Inductive construction of the p-adic zeta functions for noncommutative p-extensions of exponent p of totally real fields." Duke Math. J. 158 (2) 247 - 305, 1 June 2011. https://doi.org/10.1215/00127094-1334013

Information

Published: 1 June 2011
First available in Project Euclid: 31 May 2011

zbMATH: 1238.11100
MathSciNet: MR2805070
Digital Object Identifier: 10.1215/00127094-1334013

Subjects:
Primary: 11R23
Secondary: 11R42 , 11R80 , 19B28

Rights: Copyright © 2011 Duke University Press

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Vol.158 • No. 2 • 1 June 2011
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